Question

If a cannonball is launched off a 80m high cliff with no vertical velocity, and a 10m/s horizontal velocity, what will the cannon ball’s displacement be after it hits the ground?

Answer 1

The cannonball's displacement after it hits the ground is approximately 40.4 meters horizontally away from the base of the cliff, calculated by finding the time it takes to fall 80 meters and using that time to determine the horizontal distance traveled.

Step-by-step explanation:

To determine the cannonball's displacement after it hits the ground, we need to calculate the time it takes for the cannonball to fall 80 meters and use that time to find out how far it travels horizontally. Since there is no vertical velocity, we can use the equation for the distance traveled under constant acceleration due to gravity (g = 9.81 m/s2).

The time (t) it takes to fall can be found using the formula:
h = 0.5 * g * t2

Solving for time,
t = sqrt(2 * h / g)
Substituting h = 80 m,
t = sqrt(2 * 80 m / 9.81 m/s2)
t ≈ 4.04 s

Now, to find the horizontal displacement (x), we use the constant horizontal velocity (vx) and the time calculated:
x = vx * t
Substituting vx = 10 m/s,
x = 10 m/s * 4.04 s
x = 40.4 m

Therefore, the cannonball's displacement after it hits the ground is approximately 40.4 meters horizontally away from the base of the cliff.